Subgroups — C₂×C₃×#66022 #14480124

Order 1920.

2336 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×#125	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×#66022	C₂	1	16	yes	maximal, direct product factor
3	C₂×C₃×#4042	C₂	1	4	yes	maximal
4	C₂×C₃×#4038	C₂	1	2	yes	maximal
5	C₂×C₃×#4034	C₂	1	2	yes	maximal, complemented
6	C₂×C₃×#4033	C₂	1	4	yes	maximal, complemented
7	C₂×C₃×C₄²×D₅	C₂	1	1	yes	maximal, characteristic
8	C₂×C₃×#4016	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#66022	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₂²×C₃×C₄×D₅	C₂²	1	2	yes	—
11	C₂²×C₃×C₄×D₅	C₂²	1	1	yes	characteristic
12	C₂²×C₃×Dic₁₀	C₂²	1	4	yes	—
13	C₃×C₅×#125	C₂²	1	8	yes	complemented
14	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	4	yes	—
15	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
16	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
17	C₂×C₃×#685	C₂²	1	4	yes	—
18	C₂×C₃×C₄⋊Dic₅	C₂²	1	2	yes	—
19	C₂×C₃×#683	C₂²	1	4	yes	—
20	C₂×C₃×#683	C₂²	1	4	yes	—
21	C₂×C₃×C₄×Dic₅	C₂²	1	2	yes	—
22	C₂×C₃×C₄×Dic₅	C₂²	1	1	yes	characteristic
23	C₂×C₃×C₄×Dic₅	C₂²	1	4	yes	—
24	C₃×#4042	C₂²	1	32	yes	—
25	C₃×#4038	C₂²	1	16	yes	—
26	C₃×#4034	C₂²	1	16	yes	complemented
27	C₃×#4033	C₂²	1	32	yes	complemented
28	C₃×C₄²×D₅	C₂²	1	8	yes	—
29	C₃×#4016	C₂²	1	8	yes	complemented
30	C₂×C₃×#533	—	5	1	no	maximal, Hall
31	C₂×C₅×#125	C₂×C₃	1	1	yes	characteristic, complemented
32	#66022	C₂×C₃	1	16	yes	direct product factor
33	C₂×#4042	C₂×C₃	1	4	yes	—
34	C₂×#4038	C₂×C₃	1	2	yes	—
35	C₂×#4034	C₂×C₃	1	2	yes	complemented
36	C₂×#4033	C₂×C₃	1	4	yes	complemented
37	C₂×C₄²×D₅	C₂×C₃	1	1	yes	characteristic
38	C₂×#4016	C₂×C₃	1	1	yes	characteristic, complemented
39	C₂³×C₃×D₅	C₂³	1	1	yes	characteristic
40	C₂²×C₃×C₄×C₅	C₂³	1	4	yes	—
41	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
42	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
43	C₂²×C₃×Dic₅	C₂³	1	4	yes	—
44	C₂²×C₃×Dic₅	C₂³	1	1	yes	characteristic
45	C₂²×C₃×Dic₅	C₂³	1	2	yes	—
46	C₂×C₃×C₄×D₅	—	2	8	no	—
47	C₂×C₃×C₄×D₅	Q₈	1	8	yes	complemented
48	C₂×C₃×C₄×D₅	C₂³	1	8	yes	—
49	C₂×C₃×C₄×D₅	C₂³	1	4	yes	—
50	C₂×C₃×Dic₁₀	—	2	16	no	—
51	C₂×C₃×Dic₁₀	C₂³	1	16	yes	—
52	C₃×C₅×C₄⋊C₄	C₂³	1	16	yes	—
53	C₃×C₅×C₄⋊C₄	C₂³	1	8	yes	—
54	C₃×C₄²×C₅	C₂³	1	4	yes	—
55	C₃×#685	C₂³	1	16	yes	—
56	C₃×C₄⋊Dic₅	C₂³	1	8	yes	—
57	C₃×#683	C₂³	1	16	yes	—
58	C₃×#683	C₂³	1	16	yes	—
59	C₃×C₄×Dic₅	C₂³	1	8	yes	—
60	C₃×C₄×Dic₅	C₂³	1	4	yes	—
61	C₃×C₄×Dic₅	C₂³	1	16	yes	—
62	C₃×#533	—	5	16	no	—
63	C₂×C₃×C₄⋊Q₈	—	5	2	no	—
64	C₂×C₃×#125	—	5	1	no	—
65	C₂×C₃×#125	D₅	1	1	yes	characteristic, complemented
66	C₂×C₃×C₂²⋊Q₈	—	5	4	no	—
67	C₂×C₃×C₄×Q₈	—	5	4	no	—
68	C₂×C₃×#117	—	5	2	no	—
69	C₂²×C₃×C₄²	—	5	1	no	—
70	C₂²×C₄×D₅	C₂²×C₃	1	2	yes	—
71	C₂²×C₄×D₅	C₂²×C₃	1	1	yes	characteristic
72	C₂²×Dic₁₀	C₂²×C₃	1	4	yes	—
73	C₅×#125	C₂²×C₃	1	8	yes	complemented
74	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	4	yes	—
75	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
76	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
77	C₂×#685	C₂²×C₃	1	4	yes	—
78	C₂×C₄⋊Dic₅	C₂²×C₃	1	2	yes	—
79	C₂×#683	C₂²×C₃	1	4	yes	—
80	C₂×#683	C₂²×C₃	1	4	yes	—
81	C₂×C₄×Dic₅	C₂²×C₃	1	2	yes	—
82	C₂×C₄×Dic₅	C₂²×C₃	1	1	yes	characteristic
83	C₂×C₄×Dic₅	C₂²×C₃	1	4	yes	—
84	#4042	C₂²×C₃	1	32	yes	—
85	#4038	C₂²×C₃	1	16	yes	—
86	#4034	C₂²×C₃	1	16	yes	complemented
87	#4033	C₂²×C₃	1	32	yes	complemented
88	C₄²×D₅	C₂²×C₃	1	8	yes	—
89	#4016	C₂²×C₃	1	8	yes	complemented
90	C₂×#533	—	5	1	no	Sylow
91	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
92	C₂²×C₃×D₅	—	2	4	no	—
93	C₂²×C₃×D₅	C₂×Q₈	1	4	yes	—
94	C₂²×C₃×D₅	C₂⁴	1	2	yes	—
95	C₂×C₃×C₄×C₅	—	2	8	no	—
96	C₂×C₃×C₄×C₅	—	2	4	no	—
97	C₂×C₃×C₄×C₅	C₂×Q₈	1	4	yes	—
98	C₂×C₃×C₄×C₅	C₂⁴	1	4	yes	—
99	C₂×C₃×C₄×C₅	C₂⁴	1	8	yes	—
100	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
101	C₂×C₃×Dic₅	—	2	8	no	—
102	C₂×C₃×Dic₅	C₂×Q₈	1	4	yes	—
103	C₂×C₃×Dic₅	#41	1	8	yes	—
104	C₂×C₃×Dic₅	C₂⁴	1	8	yes	—
105	C₂×C₃×Dic₅	C₂⁴	1	2	yes	—
106	C₂×C₃×Dic₅	C₂⁴	1	4	yes	—
107	C₃×C₄×D₅	—	2	16	no	—
108	C₃×C₄×D₅	C₂×Q₈	1	16	yes	complemented
109	C₃×Dic₁₀	—	2	32	no	—
110	C₂²×C₃×Q₈	—	5	4	no	—
111	C₂³×C₃×C₄	—	5	1	no	—
112	C₂³×C₃×C₄	—	5	2	no	—
113	C₃×C₄⋊Q₈	—	5	16	no	—
114	C₃×#125	—	5	8	no	—
115	C₃×#125	C₂×D₅	1	8	yes	complemented
116	C₃×C₂²⋊Q₈	—	5	32	no	—
117	C₃×C₄×Q₈	—	5	32	no	—
118	C₃×#117	—	5	16	no	—
119	C₂×C₃×C₄⋊C₄	—	5	2	no	—
120	C₂×C₃×C₄⋊C₄	—	5	4	no	—
121	C₂×C₃×C₄⋊C₄	—	5	4	no	—
122	C₂×C₃×C₄⋊C₄	C₂×D₅	1	2	yes	—
123	C₂×C₃×C₄⋊C₄	C₂×D₅	1	4	yes	—
124	C₂×C₃×C₂²⋊C₄	—	5	4	no	—
125	C₂×C₃×C₄²	—	5	2	no	—
126	C₂×C₃×C₄²	—	5	1	no	—
127	C₂×C₃×C₄²	—	5	4	no	—
128	C₂×C₃×C₄²	—	5	8	no	—
129	C₂×C₃×C₄²	C₂×D₅	1	1	yes	characteristic
130	C₂³×D₅	C₂³×C₃	1	1	yes	characteristic
131	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
132	C₂²×C₄×C₅	C₂³×C₃	1	4	yes	—
133	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
134	C₂²×Dic₅	C₂³×C₃	1	4	yes	—
135	C₂²×Dic₅	C₂³×C₃	1	1	yes	characteristic
136	C₂²×Dic₅	C₂³×C₃	1	2	yes	—
137	C₂×C₄×D₅	—	2	8	no	—
138	C₂×C₄×D₅	C₃×Q₈	1	8	yes	complemented
139	C₂×C₄×D₅	C₂³×C₃	1	8	yes	—
140	C₂×C₄×D₅	C₂³×C₃	1	4	yes	—
141	C₂×Dic₁₀	—	2	16	no	—
142	C₂×Dic₁₀	C₂³×C₃	1	16	yes	—
143	C₅×C₄⋊C₄	C₂³×C₃	1	16	yes	—
144	C₅×C₄⋊C₄	C₂³×C₃	1	8	yes	—
145	C₄²×C₅	C₂³×C₃	1	4	yes	—
146	#685	C₂³×C₃	1	16	yes	—
147	C₄⋊Dic₅	C₂³×C₃	1	8	yes	—
148	#683	C₂³×C₃	1	16	yes	—
149	#683	C₂³×C₃	1	16	yes	—
150	C₄×Dic₅	C₂³×C₃	1	8	yes	—
151	C₄×Dic₅	C₂³×C₃	1	4	yes	—
152	C₄×Dic₅	C₂³×C₃	1	16	yes	—
153	#533	—	5	16	no	—
154	C₂×C₄⋊Q₈	—	5	2	no	—
155	C₂×#125	—	5	1	no	—
156	C₂×#125	C₃×D₅	1	1	yes	characteristic, complemented
157	C₂×C₂²⋊Q₈	—	5	4	no	—
158	C₂×C₄×Q₈	—	5	4	no	—
159	C₂×#117	—	5	2	no	—
160	C₂²×C₄²	—	5	1	no	—
161	C₂²×C₃×C₅	C₂²×Q₈	1	2	yes	—
162	C₂²×C₃×C₅	C₂×#41	1	4	yes	—
163	C₂²×C₃×C₅	C₂⁵	1	1	yes	characteristic
164	C₂×C₃×D₅	—	2	8	no	—
165	C₂×C₃×D₅	—	2	4	no	—
166	C₂×C₃×D₅	C₂²×Q₈	1	4	yes	—
167	C₃×C₄×C₅	—	2	8	no	—
168	C₃×C₄×C₅	—	2	4	no	—
169	C₃×C₄×C₅	C₂²×Q₈	1	4	yes	—
170	C₃×Dic₅	—	2	8	no	—
171	C₃×Dic₅	C₂²×Q₈	1	4	yes	—
172	C₃×Dic₅	C₂×#41	1	8	yes	—
173	C₂⁴×C₃	—	5	1	no	—
174	C₂×C₃×Q₈	—	5	16	no	—
175	C₂×C₃×Q₈	—	10	16	no	—
176	C₂²×C₃×C₄	—	5	1	no	—
177	C₂²×C₃×C₄	—	5	2	no	—
178	C₂²×C₃×C₄	—	5	8	no	—
179	C₂²×C₃×C₄	—	5	4	no	—
180	C₂²×C₃×C₄	—	5	4	no	—
181	C₂²×C₃×C₄	—	5	8	no	—
182	C₂²×C₃×C₄	—	10	8	no	—
183	C₂²×C₃×C₄	C₂²×D₅	1	2	yes	—
184	C₂²×C₃×C₄	C₂²×D₅	1	4	yes	—
185	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
186	C₃×C₄⋊C₄	—	5	16	no	—
187	C₃×C₄⋊C₄	—	5	16	no	—
188	C₃×C₄⋊C₄	—	5	8	no	—
189	C₃×C₄⋊C₄	C₂²×D₅	1	8	yes	—
190	C₃×C₄⋊C₄	C₂²×D₅	1	16	yes	—
191	C₃×C₂²⋊C₄	—	5	16	no	—
192	C₃×C₄²	—	5	8	no	—
193	C₃×C₄²	—	5	4	no	—
194	C₃×C₄²	—	5	16	no	—
195	C₃×C₄²	C₂²×D₅	1	4	yes	—
196	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
197	C₂²×D₅	—	2	4	no	—
198	C₂²×D₅	C₂×C₃×Q₈	1	4	yes	—
199	C₂²×D₅	C₂⁴×C₃	1	2	yes	—
200	C₂×C₄×C₅	—	2	8	no	—
201	C₂×C₄×C₅	—	2	4	no	—
202	C₂×C₄×C₅	C₂×C₃×Q₈	1	4	yes	—
203	C₂×C₄×C₅	C₂⁴×C₃	1	4	yes	—
204	C₂×C₄×C₅	C₂⁴×C₃	1	8	yes	—
205	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
206	C₂×Dic₅	—	2	8	no	—
207	C₂×Dic₅	C₂×C₃×Q₈	1	4	yes	—
208	C₂×Dic₅	C₃×#41	1	8	yes	—
209	C₂×Dic₅	C₂⁴×C₃	1	8	yes	—
210	C₂×Dic₅	C₂⁴×C₃	1	2	yes	—
211	C₂×Dic₅	C₂⁴×C₃	1	4	yes	—
212	C₄×D₅	—	2	16	no	—
213	C₄×D₅	C₂×C₃×Q₈	1	16	yes	complemented
214	Dic₁₀	—	2	32	no	—
215	C₂²×Q₈	—	5	4	no	—
216	C₂³×C₄	—	5	1	no	—
217	C₂³×C₄	—	5	2	no	—
218	C₄⋊Q₈	—	5	16	no	—
219	#125	—	5	8	no	—
220	#125	C₂×C₃×D₅	1	8	yes	complemented
221	C₂²⋊Q₈	—	5	32	no	—
222	C₄×Q₈	—	5	32	no	—
223	#117	—	5	16	no	—
224	C₂×C₄⋊C₄	—	5	2	no	—
225	C₂×C₄⋊C₄	—	5	4	no	—
226	C₂×C₄⋊C₄	—	5	4	no	—
227	C₂×C₄⋊C₄	C₂×C₃×D₅	1	2	yes	—
228	C₂×C₄⋊C₄	C₂×C₃×D₅	1	4	yes	—
229	C₂×C₂²⋊C₄	—	5	4	no	—
230	C₂×C₄²	—	5	4	no	—
231	C₂×C₄²	—	5	2	no	—
232	C₂×C₄²	—	5	1	no	—
233	C₂×C₄²	—	5	8	no	—
234	C₂×C₄²	C₂×C₃×D₅	1	1	yes	characteristic
235	C₂×C₃×C₅	#533	1	4	yes	complemented
236	C₂×C₃×C₅	C₂³×Q₈	1	1	yes	characteristic
237	C₂×C₃×C₅	C₂²×#41	1	2	yes	—
238	C₃×D₅	—	2	4	no	—
239	C₂³×C₃	—	5	4	no	—
240	C₂³×C₃	—	5	2	no	—
241	C₂³×C₃	—	10	4	no	—
242	C₂³×C₃	C₂³×D₅	1	1	yes	characteristic
243	C₃×Q₈	—	10	32	no	—
244	C₂×C₃×C₄	—	2	4	no	—
245	C₂×C₃×C₄	—	2	8	no	—
246	C₂×C₃×C₄	—	5	4	no	—
247	C₂×C₃×C₄	—	5	8	no	—
248	C₂×C₃×C₄	—	5	2	no	—
249	C₂×C₃×C₄	—	5	4	no	—
250	C₂×C₃×C₄	—	5	16	no	—
251	C₂×C₃×C₄	—	5	8	no	—
252	C₂×C₃×C₄	—	10	16	no	—
253	C₂×C₃×C₄	—	10	8	no	—
254	C₂×C₃×C₄	Q₈×D₅	1	4	yes	—
255	C₂×C₃×C₄	C₂³×D₅	1	4	yes	—
256	C₂×C₃×C₄	C₂³×D₅	1	8	yes	—
257	C₂×C₃×C₄	C₂³×D₅	1	2	yes	—
258	C₂²×C₅	C₂²×C₃×Q₈	1	2	yes	—
259	C₂²×C₅	C₂×C₃×#41	1	4	yes	—
260	C₂²×C₅	C₂⁵×C₃	1	1	yes	characteristic
261	C₂×D₅	—	2	4	no	—
262	C₂×D₅	—	2	8	no	—
263	C₂×D₅	C₂²×C₃×Q₈	1	4	yes	—
264	C₄×C₅	—	2	8	no	—
265	C₄×C₅	—	2	4	no	—
266	C₄×C₅	C₂²×C₃×Q₈	1	4	yes	—
267	Dic₅	—	2	8	no	—
268	Dic₅	C₂²×C₃×Q₈	1	4	yes	—
269	Dic₅	C₂×C₃×#41	1	8	yes	—
270	C₂⁴	—	5	1	no	—
271	C₂×Q₈	—	5	16	no	—
272	C₂×Q₈	—	10	16	no	—
273	C₂²×C₄	—	5	1	no	—
274	C₂²×C₄	—	5	2	no	—
275	C₂²×C₄	—	5	8	no	—
276	C₂²×C₄	—	5	4	no	—
277	C₂²×C₄	—	5	4	no	—
278	C₂²×C₄	—	5	8	no	—
279	C₂²×C₄	—	10	8	no	—
280	C₂²×C₄	C₂²×C₃×D₅	1	2	yes	—
281	C₂²×C₄	C₂²×C₃×D₅	1	4	yes	—
282	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
283	C₄⋊C₄	—	5	8	no	—
284	C₄⋊C₄	—	5	16	no	—
285	C₄⋊C₄	—	5	16	no	—
286	C₄⋊C₄	C₂²×C₃×D₅	1	8	yes	—
287	C₄⋊C₄	C₂²×C₃×D₅	1	16	yes	—
288	C₂²⋊C₄	—	5	16	no	—
289	C₄²	—	5	8	no	—
290	C₄²	—	5	4	no	—
291	C₄²	—	5	16	no	—
292	C₄²	C₂²×C₃×D₅	1	4	yes	—
293	C₃×C₅	C₂×#533	1	1	yes	characteristic, complemented, Hall
294	C₂²×C₃	—	5	4	no	—
295	C₂²×C₃	—	10	8	no	—
296	C₂²×C₃	—	10	4	no	—
297	C₂²×C₃	C₂×Q₈×D₅	1	2	yes	—
298	C₂²×C₃	D₅×#41	1	4	yes	—
299	C₂²×C₃	C₂⁴×D₅	1	1	yes	characteristic
300	C₃×C₄	—	2	4	no	—
301	C₃×C₄	—	2	8	no	—
302	C₃×C₄	—	5	4	no	—
303	C₃×C₄	—	5	8	no	—
304	C₃×C₄	—	10	8	no	—
305	C₃×C₄	C₂×Q₈×D₅	1	4	yes	—
306	C₂×C₅	C₃×#533	1	4	yes	complemented
307	C₂×C₅	C₂³×C₃×Q₈	1	1	yes	characteristic
308	C₂×C₅	C₂²×C₃×#41	1	2	yes	—
309	D₅	—	2	4	no	—
310	C₂³	—	5	4	no	—
311	C₂³	—	5	2	no	—
312	C₂³	—	10	4	no	—
313	C₂³	C₂³×C₃×D₅	1	1	yes	characteristic
314	Q₈	—	10	32	no	—
315	C₂×C₄	—	2	4	no	—
316	C₂×C₄	—	2	8	no	—
317	C₂×C₄	—	5	4	no	—
318	C₂×C₄	—	5	8	no	—
319	C₂×C₄	—	5	2	no	—
320	C₂×C₄	—	5	4	no	—
321	C₂×C₄	—	5	16	no	—
322	C₂×C₄	—	5	8	no	—
323	C₂×C₄	—	10	16	no	—
324	C₂×C₄	—	10	8	no	—
325	C₂×C₄	C₃×Q₈×D₅	1	4	yes	—
326	C₂×C₄	C₂³×C₃×D₅	1	4	yes	—
327	C₂×C₄	C₂³×C₃×D₅	1	8	yes	—
328	C₂×C₄	C₂³×C₃×D₅	1	2	yes	—
329	C₂×C₃	—	10	4	no	—
330	C₂×C₃	#66022	1	4	yes	direct product factor
331	C₂×C₃	C₂²×Q₈×D₅	1	1	yes	characteristic
332	C₂×C₃	C₂×D₅×#41	1	2	yes	—
333	C₅	C₂×C₃×#533	1	1	yes	characteristic, complemented, Sylow
334	C₂²	—	5	4	no	—
335	C₂²	—	10	4	no	—
336	C₂²	—	10	8	no	—
337	C₂²	C₂×C₃×Q₈×D₅	1	2	yes	—
338	C₂²	C₃×D₅×#41	1	4	yes	—
339	C₂²	C₂⁴×C₃×D₅	1	1	yes	characteristic
340	C₄	—	2	4	no	—
341	C₄	—	2	8	no	—
342	C₄	—	5	4	no	—
343	C₄	—	5	8	no	—
344	C₄	—	10	8	no	—
345	C₄	C₂×C₃×Q₈×D₅	1	4	yes	—
346	C₃	C₂×#66022	1	1	yes	characteristic, direct product factor, Sylow
347	C₂	—	10	4	no	—
348	C₂	C₃×#66022	1	4	yes	direct product factor
349	C₂	C₂²×C₃×Q₈×D₅	1	1	yes	characteristic
350	C₂	C₂×C₃×D₅×#41	1	2	yes	—

	subgroup	G/H
center	C₂³×C₃	C₂³×D₅
commutator, cosocle	C₂²×C₅	C₂⁵×C₃
Frattini	C₂²	C₂⁴×C₃×D₅
Fitting	C₂×C₃×C₅×#125	C₂
socle	C₂³×C₃×C₅	C₂⁴
prime radical	C₂³×C₃×D₅	C₂³
hypercenter	C₂×C₃×#125	D₅
hypocenter	C₅	C₂×C₃×#533
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂³×C₃ ◁ C₂×C₃×#125

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₂×C₃×C₅×#125	C₂	semidirect
2. C₃×#66022	C₂	direct (N × H)
5. C₂×C₃×#4034	C₂	semidirect
6. C₂×C₃×#4033	C₂	semidirect
8. C₂×C₃×#4016	C₂	semidirect
9. C₂×#66022	C₃	direct (N × H)
13. C₃×C₅×#125	C₂²	semidirect
26. C₃×#4034	C₂²	semidirect
27. C₃×#4033	C₂²	semidirect
29. C₃×#4016	C₂²	semidirect
31. C₂×C₅×#125	C₂×C₃	semidirect
32. #66022	C₂×C₃	direct (N × H)
35. C₂×#4034	C₂×C₃	semidirect
36. C₂×#4033	C₂×C₃	semidirect
38. C₂×#4016	C₂×C₃	semidirect
47. C₂×C₃×C₄×D₅	Q₈	semidirect
65. C₂×C₃×#125	D₅	semidirect
73. C₅×#125	C₂²×C₃	semidirect
86. #4034	C₂²×C₃	semidirect
87. #4033	C₂²×C₃	semidirect
89. #4016	C₂²×C₃	semidirect
108. C₃×C₄×D₅	C₂×Q₈	semidirect
115. C₃×#125	C₂×D₅	semidirect
138. C₂×C₄×D₅	C₃×Q₈	semidirect
156. C₂×#125	C₃×D₅	semidirect
213. C₄×D₅	C₂×C₃×Q₈	semidirect
220. #125	C₂×C₃×D₅	semidirect
235. C₂×C₃×C₅	#533	semidirect
293. C₃×C₅	C₂×#533	semidirect
306. C₂×C₅	C₃×#533	semidirect
330. C₂×C₃	#66022	direct (N × H)
333. C₅	C₂×C₃×#533	semidirect
346. C₃	C₂×#66022	direct (N × H)
348. C₂	C₃×#66022	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₃×C₅×#125	2
C₃×#66022	2
C₂×C₃×#4042	2
C₂×C₃×#4038	2
C₂×C₃×#4034	2
C₂×C₃×#4033	2
C₂×C₃×C₄²×D₅	2
C₂×C₃×#4016	2
C₂×#66022	3
C₂×C₃×#533	5

Subgroups — C2×C3×#66022 #14480124

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#66022 #14480124